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Rabinowitz Floer homology for prequantization bundles and Floer Gysin sequence 预量化束的拉比诺维兹-弗洛尔同源性和弗洛尔-吉辛序列
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-05-09 DOI: 10.1007/s00208-024-02878-w
Joonghyun Bae, Jungsoo Kang, Sungho Kim
{"title":"Rabinowitz Floer homology for prequantization bundles and Floer Gysin sequence","authors":"Joonghyun Bae, Jungsoo Kang, Sungho Kim","doi":"10.1007/s00208-024-02878-w","DOIUrl":"https://doi.org/10.1007/s00208-024-02878-w","url":null,"abstract":"<p>Let <i>Y</i> be a prequantization bundle over a closed spherically monotone symplectic manifold <span>(Sigma )</span>. Adapting an idea due to Diogo and Lisi, we study a split version of Rabinowitz Floer homology for <i>Y</i> in the following two settings. First, <span>(Sigma )</span> is a symplectic hyperplane section of a closed symplectic manifold <i>X</i> satisfying a certain monotonicity condition; in this case, <span>(X {{setminus }} Sigma )</span> is a Liouville filling of <i>Y</i>. Second, the minimal Chern number of <span>(Sigma )</span> is greater than one, which is the case where the Rabinowitz Floer homology of the symplectization <span>(mathbb {R} times Y)</span> is defined. In both cases, we construct a Gysin-type exact sequence connecting the Rabinowitz Floer homology of <span>(X{setminus }Sigma )</span> or <span>(mathbb {R} times Y)</span> and the quantum homology of <span>(Sigma )</span>. As applications, we discuss the invertibility of a symplectic hyperplane section class in quantum homology, the isotopy problem for fibered Dehn twists, the orderability problem for prequantization bundles, and the existence of translated points. We also provide computational results based on the exact sequence that we construct.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"161 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140936314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solutions with moving singularities for a one-dimensional nonlinear diffusion equation 一维非线性扩散方程的移动奇点解决方案
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-05-08 DOI: 10.1007/s00208-024-02882-0
Marek Fila, Jin Takahashi, Eiji Yanagida
{"title":"Solutions with moving singularities for a one-dimensional nonlinear diffusion equation","authors":"Marek Fila, Jin Takahashi, Eiji Yanagida","doi":"10.1007/s00208-024-02882-0","DOIUrl":"https://doi.org/10.1007/s00208-024-02882-0","url":null,"abstract":"<p>The aim of this paper is to study singular solutions for a one-dimensional nonlinear diffusion equation. Due to slow diffusion near singular points, there exists a solution with a singularity at a prescribed position depending on time. To study properties of such singular solutions, we define a minimal singular solution as a limit of a sequence of approximate solutions with large Dirichlet data. Applying the comparison principle and the intersection number argument, we discuss the existence and uniqueness of a singular solution for an initial-value problem, the profile near singular points and large-time behavior of solutions. We also give some results concerning the appearance of a burning core, convergence to traveling waves and the existence of an entire solution.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"10 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140936341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A biharmonic analogue of the Alt–Caffarelli problem 阿尔特-卡法雷利问题的双谐波类似物
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-05-06 DOI: 10.1007/s00208-024-02883-z
Hans-Christoph Grunau, Marius Müller
{"title":"A biharmonic analogue of the Alt–Caffarelli problem","authors":"Hans-Christoph Grunau, Marius Müller","doi":"10.1007/s00208-024-02883-z","DOIUrl":"https://doi.org/10.1007/s00208-024-02883-z","url":null,"abstract":"<p>We study a natural biharmonic analogue of the classical Alt–Caffarelli problem, both under Dirichlet and under Navier boundary conditions. We show existence, basic properties and <span>(C^{1,alpha })</span>-regularity of minimisers. For the Navier problem we also obtain a symmetry result in case that the boundary data are radial. We find this remarkable because the problem under investigation is of higher order. Computing radial minimisers explicitly we find that the obtained regularity is optimal.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"24 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Flux and symmetry effects on quantum tunneling 量子隧道的通量和对称效应
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-05-05 DOI: 10.1007/s00208-024-02874-0
Bernard Helffer, Ayman Kachmar, Mikael Persson Sundqvist
{"title":"Flux and symmetry effects on quantum tunneling","authors":"Bernard Helffer, Ayman Kachmar, Mikael Persson Sundqvist","doi":"10.1007/s00208-024-02874-0","DOIUrl":"https://doi.org/10.1007/s00208-024-02874-0","url":null,"abstract":"<p>Motivated by the analysis of the tunneling effect for the magnetic Laplacian, we introduce an abstract framework for the spectral reduction of a self-adjoint operator to a hermitian matrix. We illustrate this framework by three applications, firstly the electro-magnetic Laplacian with constant magnetic field and three equidistant potential wells, secondly a pure constant magnetic field and Neumann boundary condition in a smoothed triangle, and thirdly a magnetic step where the discontinuity line is a smoothed triangle. Flux effects are visible in the three aforementioned settings through the occurrence of eigenvalue crossings. Moreover, in the electro-magnetic Laplacian setting with double well radial potential, we rule out an artificial condition on the distance of the wells and extend the range of validity for the tunneling approximation recently established in Fefferman et al. (SIAM J Math Anal 54: 1105–1130, 2022), Helffer &amp; Kachmar (Pure Appl Anal, 2024), thereby settling the problem of electro-magnetic tunneling under constant magnetic field and a sum of translated radial electric potentials.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"81 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889703","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
$$L^p$$ bounds for Stein’s spherical maximal operators 斯坦因球面最大算子的 $L^p$$ 边界
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-05-04 DOI: 10.1007/s00208-024-02884-y
Naijia Liu, Minxing Shen, Liang Song, Lixin Yan
{"title":"$$L^p$$ bounds for Stein’s spherical maximal operators","authors":"Naijia Liu, Minxing Shen, Liang Song, Lixin Yan","doi":"10.1007/s00208-024-02884-y","DOIUrl":"https://doi.org/10.1007/s00208-024-02884-y","url":null,"abstract":"<p>Let <span>({mathfrak {M}}^alpha )</span> be the spherical maximal operators of complex order <span>(alpha )</span> on <span>({{mathbb {R}}^n})</span>. In this article we show that when <span>(nge 2)</span>, suppose </p><span>$$begin{aligned} Vert {mathfrak {M}}^{alpha } f Vert _{L^p({{mathbb {R}}^n})} le CVert f Vert _{L^p({{mathbb {R}}^n})} end{aligned}$$</span><p>holds for some <span>(alpha )</span> and <span>(pge 2)</span>, then we must have that <span>(textrm{Re},alpha ge max {1/p-(n-1)/2, -(n-1)/p }.)</span> In particular, when <span>(n=2)</span>, we prove that <span>( Vert {mathfrak {M}}^{alpha } f Vert _{L^p({{mathbb {R}}^2})} le CVert f Vert _{L^p({{mathbb {R}}^2})})</span> if <span>(textrm{Re} ! alpha &gt;max {1/p-1/2, -1/p})</span>, and consequently the range of <span>(alpha )</span> is sharp in the sense that the estimate fails for <span>(textrm{Re} alpha &lt;max {1/p-1/2, -1/ p}.)</span></p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"42 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Studying Hilbert’s 10th problem via explicit elliptic curves 通过显式椭圆曲线研究希尔伯特第 10 个问题
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-05-04 DOI: 10.1007/s00208-024-02879-9
Debanjana Kundu, Antonio Lei, Florian Sprung
{"title":"Studying Hilbert’s 10th problem via explicit elliptic curves","authors":"Debanjana Kundu, Antonio Lei, Florian Sprung","doi":"10.1007/s00208-024-02879-9","DOIUrl":"https://doi.org/10.1007/s00208-024-02879-9","url":null,"abstract":"<p>N. García-Fritz and H. Pasten showed that Hilbert’s 10th problem is unsolvable in the ring of integers of number fields of the form <span>(mathbb {Q}(root 3 of {p},sqrt{-q}))</span> for positive proportions of primes <i>p</i> and <i>q</i>. We improve their proportions and extend their results to the case of number fields of the form <span>(mathbb {Q}(root 3 of {p},sqrt{Dq}))</span>, where <i>D</i> belongs to an explicit family of positive square-free integers. We achieve this by using multiple elliptic curves, and replace their Iwasawa theory arguments by a more direct method.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"49 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Surface quasi-geostrophic equation perturbed by derivatives of space-time white noise 受时空白噪声导数扰动的表面准地转方程
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-05-03 DOI: 10.1007/s00208-024-02881-1
Martina Hofmanová, Xiaoyutao Luo, Rongchan Zhu, Xiangchan Zhu
{"title":"Surface quasi-geostrophic equation perturbed by derivatives of space-time white noise","authors":"Martina Hofmanová, Xiaoyutao Luo, Rongchan Zhu, Xiangchan Zhu","doi":"10.1007/s00208-024-02881-1","DOIUrl":"https://doi.org/10.1007/s00208-024-02881-1","url":null,"abstract":"<p>We consider a family of singular surface quasi-geostrophic equations </p><span>$$begin{aligned} partial _{t}theta +ucdot nabla theta =-nu (-Delta )^{gamma /2}theta +(-Delta )^{alpha /2}xi ,qquad u=nabla ^{perp }(-Delta )^{-1/2}theta , end{aligned}$$</span><p>on <span>([0,infty )times {mathbb {T}}^{2})</span>, where <span>(nu geqslant 0)</span>, <span>(gamma in [0,3/2))</span>, <span>(alpha in [0,1/4))</span> and <span>(xi )</span> is a space-time white noise. For the first time, we establish the <i>existence of infinitely many non-Gaussian</i></p><ul>\u0000<li>\u0000<p>probabilistically strong solutions for every initial condition in <span>(C^{eta })</span>, <span>(eta &gt;1/2)</span>;</p>\u0000</li>\u0000<li>\u0000<p>ergodic stationary solutions.</p>\u0000</li>\u0000</ul><p> The result presents a single approach applicable in the subcritical, critical as well as supercritical regime in the sense of Hairer (Invent Math 198(2):269–504, 2014). It also applies in the particular setting <span>(alpha =gamma /2)</span> which formally possesses a Gaussian invariant measure. In our proof, we first introduce a modified Da Prato–Debussche trick which, on the one hand, permits to convert irregularity in time into irregularity in space and, on the other hand, increases the regularity of the linear solution. Second, we develop a convex integration iteration for the corresponding nonlinear equation which yields non-unique non-Gaussian solutions satisfying powerful global-in-time estimates and generating stationary as well as ergodic stationary solutions.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"116 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Correction to: Positivity of anticanonical divisor in algebraic fibre spaces 更正：代数纤维空间中反偶函数除数的正相关性
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-05-03 DOI: 10.1007/s00208-024-02846-4
Chi-Kang Chang
{"title":"Correction to: Positivity of anticanonical divisor in algebraic fibre spaces","authors":"Chi-Kang Chang","doi":"10.1007/s00208-024-02846-4","DOIUrl":"https://doi.org/10.1007/s00208-024-02846-4","url":null,"abstract":"","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"10 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Localizations for quiver Hecke algebras III 矢量赫克代数的局部化 III
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-05-03 DOI: 10.1007/s00208-024-02875-z
Masaki Kashiwara, Myungho Kim, Se-jin Oh, Euiyong Park
{"title":"Localizations for quiver Hecke algebras III","authors":"Masaki Kashiwara, Myungho Kim, Se-jin Oh, Euiyong Park","doi":"10.1007/s00208-024-02875-z","DOIUrl":"https://doi.org/10.1007/s00208-024-02875-z","url":null,"abstract":"<p>Let <i>R</i> be a quiver Hecke algebra, and let <span>(mathscr {C}_{w,v})</span> be the category of finite-dimensional graded <i>R</i>-module categorifying a <i>q</i>-deformation of the doubly-invariant algebra <span>(^{N'(w)} {mathbb {C}}[N] ^{N(v)} )</span>. In this paper, we prove that the localization <span>(widetilde{mathscr {C}}_{w,v})</span> of the category <span>(mathscr {C}_{w,v})</span> can be obtained as the localization by right braiders arising from determinantial modules. As its application, we show several interesting properties of the localized category <span>(widetilde{mathscr {C}}_{w,v} )</span> including the right rigidity.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"43 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Steinberg’s cross-section of Newton strata 斯坦伯格的牛顿地层剖面图
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-05-02 DOI: 10.1007/s00208-024-02872-2
Sian Nie
{"title":"Steinberg’s cross-section of Newton strata","authors":"Sian Nie","doi":"10.1007/s00208-024-02872-2","DOIUrl":"https://doi.org/10.1007/s00208-024-02872-2","url":null,"abstract":"<p>In this note, we introduce a natural analogue of Steinberg’s cross-section in the loop group of a reductive group <span>(textbf{G})</span>. We show this loop Steinberg’s cross-section provides a simple geometric model for the poset <span>(B(textbf{G}))</span> of Frobenius-twisted conjugacy classes (referred to as Newton strata) of the loop group. As an application, we confirms a conjecture by Ivanov on decomposing loop Delgine–Lusztig varieties of Coxeter type. This geometric model also leads to new and direct proofs of several classical results, including the converse to Mazur’s inequality, Chai’s length formula on <span>(B(textbf{G}))</span>, and a key combinatorial identity in the study affine Deligne–Lusztig varieties with finite Coxeter parts.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"2010 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140832058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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